Place a lead on a fence post
Right-click the fence post to attach the lead
Right-click the animal/mob you want to leash
Keep the lead attached by moving while holding the lead item (if applicable)
If the mob breaks free, reattach the lead to the mob and keep it within reach
To remove the lead, right-click the lead on the mob or break the fence post (if attached to it)
For boats or minecarts, place the vehicle first, then attach the lead to the vehicle and the mob if you want it to follow